what is -32 to the power of 2/5

-32^(2/5) = -4

-32^2/5

When there are fractional powers, you evaluate the number to the numerator's (top) power, and then find the denominator's (bottom) root of the number.

Or you can find the root first and then find the power, which is what I will do:

-32^2/5 = (⁵√-32)² = (-2)² = 4

Simplify the following:
-32^(1/5)^2

Multiply exponents. (32^(1/5))^2 = 32^(2/5):
-32^(2/5)

32^(2/5) = (32^2)^(1/5) = (2^10)^(1/5) = 2^2:
-2^2

2^2 = 4:
Answer: |-4